limn→0cos(sinx)−cosxx4=

limx→0cos(sinx)−cosxx4=limx→0−2x4sinsinx+x2sinsinx−x2=limx→0 −2sin⁡sin⁡x+x2sin⁡x+x2⋅sin⁡sin⁡x−x2sin⁡x−x2×sin⁡x+xxsin⁡x−xx314=−24×1×1×Ltx→0⁡sin⁡xx+1×limx→0 x−x33!+x55!….-xx3=−24×(1+1)×−16=16